A preemptive goal programming for multi-objective cooperative games: an application to multi-objective linear production

The aim of this study is to investigate the fair allocation of multi-objective cooperative games (MOCGs) using a preemptive goal programming (PGP). First, this research establishes the PGP model, where the priority factors of PGP describe the importance degrees of different objectives in MOCGs, the positive and negative deviations of PGP present the relation between the overall payoff and the worth of a coalition, and the weighting factors of negative deviations of PGP express the coalition weights of MOCGs. Second, we investigate the relationships between the solutions of the PGP model and the cores of MOCGs, including the preference core, preference p-core, and dominance core. Our analysis shows that the optimal solution of PGP belongs to the preference core, and the satisfactory solution of PGP satisfying certain conditions belongs to the dominance core or preference p-core. Finally, we demonstrate the practical and managerial relevance of our results by applying our findings to a multi-objective linear production to produce certain kinds of goods using different resources for multi-firms with varying objectives and illustrate them numerically.